The basic geometry by which a sextant works is shown in red. See http://en.wikipedia.org/wiki/Sextant for details on real-life sextants and the source of the image used here.

The two large red dots can be moved to demonstrate the operation of a sextant.
Question: Look at the arc of the sextant. From the "0" mark to the "120" mark there appear to be, in reality, only 60 degrees. Indeed, the sextant takes its name from the fact that the arc is about one sixth of a full 360-degree turn. The marks along the arc show two times the angle between the sextant's mirrors. In what sense is the angle between object 1 and object 2 really two times the angle between the mirrors? Can you prove it?